Is it possible to make the remesh modifier block size constant?
Remesh modifer use the object's bounding box to determine the size of the block (combined with the scale and the octree depth)

If you want to use just the built-in tools and no python, a possible, dirty, workaround could consist in altering each object bounding box to a fixed the one of a "remeshing box".

Create a box of the wanted size, delete faces (deleting edges is optional) and assign to the object a Remesh modifer with the target resolution.



Create/pick one object, move it inside the box. Apply scale.



Join the object with a duplicate of your cage. This way the mesh will inherit the modifiers with all the settings.



You can edit the object freely until it stays inside the box defined by the vertices.





Cons:


The box can't be changed interactively.
You have to duplicate and join the remeshing box for each object.